Subsets¶
- class sympy.combinatorics.subsets.Subset(subset, superset)[source]¶
Represents a basic subset object.
Explanation
We generate subsets using essentially two techniques, binary enumeration and lexicographic enumeration. The Subset class takes two arguments, the first one describes the initial subset to consider and the second describes the superset.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.next_binary().subset ['b'] >>> a.prev_binary().subset ['c']
- classmethod bitlist_from_subset(subset, superset)[source]¶
Gets the bitlist corresponding to a subset.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> Subset.bitlist_from_subset(['c', 'd'], ['a', 'b', 'c', 'd']) '0011'
See also
- property cardinality¶
Returns the number of all possible subsets.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.cardinality 16
See also
- iterate_binary(k)[source]¶
This is a helper function. It iterates over the binary subsets by
k
steps. This variable can be both positive or negative.Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.iterate_binary(-2).subset ['d'] >>> a = Subset(['a', 'b', 'c'], ['a', 'b', 'c', 'd']) >>> a.iterate_binary(2).subset []
See also
- iterate_graycode(k)[source]¶
Helper function used for prev_gray and next_gray. It performs
k
step overs to get the respective Gray codes.Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset([1, 2, 3], [1, 2, 3, 4]) >>> a.iterate_graycode(3).subset [1, 4] >>> a.iterate_graycode(-2).subset [1, 2, 4]
- next_binary()[source]¶
Generates the next binary ordered subset.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.next_binary().subset ['b'] >>> a = Subset(['a', 'b', 'c', 'd'], ['a', 'b', 'c', 'd']) >>> a.next_binary().subset []
See also
- next_gray()[source]¶
Generates the next Gray code ordered subset.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset([1, 2, 3], [1, 2, 3, 4]) >>> a.next_gray().subset [1, 3]
See also
- next_lexicographic()[source]¶
Generates the next lexicographically ordered subset.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.next_lexicographic().subset ['d'] >>> a = Subset(['d'], ['a', 'b', 'c', 'd']) >>> a.next_lexicographic().subset []
See also
- prev_binary()[source]¶
Generates the previous binary ordered subset.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset([], ['a', 'b', 'c', 'd']) >>> a.prev_binary().subset ['a', 'b', 'c', 'd'] >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.prev_binary().subset ['c']
See also
- prev_gray()[source]¶
Generates the previous Gray code ordered subset.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset([2, 3, 4], [1, 2, 3, 4, 5]) >>> a.prev_gray().subset [2, 3, 4, 5]
See also
- prev_lexicographic()[source]¶
Generates the previous lexicographically ordered subset.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset([], ['a', 'b', 'c', 'd']) >>> a.prev_lexicographic().subset ['d'] >>> a = Subset(['c','d'], ['a', 'b', 'c', 'd']) >>> a.prev_lexicographic().subset ['c']
See also
- property rank_binary¶
Computes the binary ordered rank.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset([], ['a','b','c','d']) >>> a.rank_binary 0 >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.rank_binary 3
See also
- property rank_gray¶
Computes the Gray code ranking of the subset.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset(['c','d'], ['a','b','c','d']) >>> a.rank_gray 2 >>> a = Subset([2, 4, 5], [1, 2, 3, 4, 5, 6]) >>> a.rank_gray 27
See also
- property rank_lexicographic¶
Computes the lexicographic ranking of the subset.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.rank_lexicographic 14 >>> a = Subset([2, 4, 5], [1, 2, 3, 4, 5, 6]) >>> a.rank_lexicographic 43
- property size¶
Gets the size of the subset.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.size 2
See also
- property subset¶
Gets the subset represented by the current instance.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.subset ['c', 'd']
See also
- classmethod subset_from_bitlist(super_set, bitlist)[source]¶
Gets the subset defined by the bitlist.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> Subset.subset_from_bitlist(['a', 'b', 'c', 'd'], '0011').subset ['c', 'd']
See also
- classmethod subset_indices(subset, superset)[source]¶
Return indices of subset in superset in a list; the list is empty if all elements of
subset
are not insuperset
.Examples
>>> from sympy.combinatorics import Subset >>> superset = [1, 3, 2, 5, 4] >>> Subset.subset_indices([3, 2, 1], superset) [1, 2, 0] >>> Subset.subset_indices([1, 6], superset) [] >>> Subset.subset_indices([], superset) []
- property superset¶
Gets the superset of the subset.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.superset ['a', 'b', 'c', 'd']
See also
- property superset_size¶
Returns the size of the superset.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> a = Subset(['c', 'd'], ['a', 'b', 'c', 'd']) >>> a.superset_size 4
See also
- classmethod unrank_binary(rank, superset)[source]¶
Gets the binary ordered subset of the specified rank.
Examples
>>> from sympy.combinatorics.subsets import Subset >>> Subset.unrank_binary(4, ['a', 'b', 'c', 'd']).subset ['b']
See also
- subsets.ksubsets(k)[source]¶
Finds the subsets of size
k
in lexicographic order.This uses the itertools generator.
Examples
>>> from sympy.combinatorics.subsets import ksubsets >>> list(ksubsets([1, 2, 3], 2)) [(1, 2), (1, 3), (2, 3)] >>> list(ksubsets([1, 2, 3, 4, 5], 2)) [(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)]
See also